The question
"I've lost 15 of my last 20 bets. Has my betting edge gone, or is this just a bad run?"
This is the question the whole of Statometrics is built around. Get it wrong one way and you abandon a good strategy at the bottom of a normal losing run. Get it wrong the other way and you keep feeding a dead one. This lesson gives you a rule that answers it without guesswork.
The idea in one sentence
Keep a running score that climbs a little every time the results look more like a dead strategy than a live one, falls back when they don't, and never drops below zero; when it crosses a line you set in advance, the edge has probably gone.
The picture
That running score is called a CUSUM, short for cumulative sum. Picture it as a bucket with a hole in it.
- Every loser pours a little water in, because losers are slightly more likely if the edge has died.
- Every winner lets water out, because winners are slightly more likely if the edge is alive.
- The bucket can't hold less than nothing, so a good spell empties it but can't bank credit for later.
- When the water reaches the line, the alarm goes.
On a live edge, winners drain the bucket a touch faster than losers fill it, so it bobs near the bottom. A normal losing run splashes some water in, then the winners take it out again. On a dead edge, the balance tips the other way and the level creeps steadily up to the line.
The chart below shows two lines. One is your profit and loss. The other is the CUSUM, with the alarm line drawn across it. The edge dies at a point you choose, and you can see how long the CUSUM takes to notice, and how often it cries wolf beforehand.
Worked Betfair example
You back selections in Match Odds at average odds of 3.0, £10 a bet, and you believe you have a +5% edge before commission. (Illustrative figures.)
- Define "alive". A 5% edge at 3.0 means a win rate of 1.05 ÷ 3.0 = 35%. After 2% commission on winnings, your ROI is 0.35 × 2 × 0.98 − 0.65 = +3.6%.
- Define "dead". Dead means the price is right: a win rate of 1 ÷ 3.0 = 33.3%. After commission, that's 0.333 × 1.96 − 0.667 = −1.3%. You must write both definitions down before you start.
- Score each result. A loser adds ln(0.667 ÷ 0.65) = +0.0253. A winner adds ln(0.333 ÷ 0.35) = −0.0488. So one winner cancels about two losers.
- Set the alarm line. Using the run lengths from the chart's simulation, a line at h = 2 gives:
- a false alarm on a live edge about once every 7,500 bets on average;
- detection of a dead edge after about 1,850 bets on average.
- Run the first ten bets.
| Bet | Result | CUSUM | Running P&L |
|---|---|---|---|
| 1 | Lost | 0.025 | −£10.00 |
| 2 | Lost | 0.051 | −£20.00 |
| 3 | Won | 0.002 | −£0.40 |
| 4 | Lost | 0.027 | −£10.40 |
| 5 | Lost | 0.053 | −£20.40 |
| 6 | Lost | 0.078 | −£30.40 |
| 7 | Lost | 0.103 | −£40.40 |
| 8 | Won | 0.054 | −£20.80 |
| 9 | Lost | 0.080 | −£30.80 |
| 10 | Lost | 0.105 | −£40.80 |
- Read it. Eight losers from ten feels awful, but the CUSUM is at 0.105, about a twentieth of the way to the line. Even 12 losers in a row only adds 0.30. A live 35% strategy has a losing run of 12 or more in about 87% of 1,000-bet spells, so this is normal.
- The honest bit. From a standing start, a dead edge takes around 1,850 bets to trip the alarm. Results alone are slow, because each bet at 3.0 swings by about £1.43 per £1 staked and a 1.7-point change in win rate is buried in that noise.
The faster way: run the CUSUM on closing line value
Now track the closing line value of every bet instead: the percentage by which your price beat Betfair's closing price. Say your live edge averages +3% CLV, a dead one averages 0%, and a single bet's CLV typically swings by about 12 points. (Illustrative figures.)
- Score each bet. Add (1.5 − CLV%) to the running total, where 1.5 is halfway between alive and dead, and floor it at zero.
- Five bets with CLV of +6, −4, +2, −10, +1 take the CUSUM to 0, 5.5, 5.0, 16.5, 17.0.
- Alarm line at 250. That gives a false alarm about once every 7,500 bets, the same as before, but a dead edge is caught after about 145 bets instead of 1,850.
Verdict: watching results, you need well over a thousand bets to tell a dead edge from a bad run. Watching CLV, you need about a hundred and fifty. This is why Statometrics measures CLV first and P&L second.
Reading the two together
| CLV | P&L | What it means |
|---|---|---|
| Holding up | Losing | A normal bad run. Keep going at normal stakes. |
| Holding up | Winning | Working as expected. |
| Fading or alarm | Winning | Luck is covering a problem. Cut stakes and investigate. |
| Fading or alarm | Losing | The edge has most likely gone. Stop. |
The formula
CUSUM on results
- S_t is the CUSUM after bet t, starting at S_0 = 0.
- x_t is the result of bet t: won or lost.
- P_alive(x_t) is the chance of that result if the edge is alive (35% for a win, 65% for a loss here).
- P_dead(x_t) is the chance if the edge is dead (33.3% and 66.7%).
In plain English: each result nudges the score towards whichever story it fits better, and the score can't go below zero.
CUSUM on CLV
- CLV_t is bet t's closing line value in percent.
- μ_alive and μ_dead are the average CLV you'd expect if the edge is alive or dead.
- r is the reference value halfway between them.
In plain English: every bet that beats the close by less than halfway between "alive" and "dead" adds to the score, and every better bet takes some away.
The alarm
- h is the threshold, chosen in advance.
In plain English: a higher line means fewer false alarms but slower detection. You pick the trade-off before you start, not in the middle of a losing run.
How it relates to a one-off test
The CUSUM is a sequential probability ratio test that restarts every time the evidence favours "alive". A one-off test asks "is there an edge?" once. The CUSUM asks "has it just stopped?" after every bet, and it's built to be checked that often, which ordinary p-values are not.
Try it
Set odds 3.0, live edge 5%, dead edge 0% and move the point where the edge dies. Count how often the CUSUM crosses the line before the edge dies (false alarms) and how long it takes after. Then switch to CLV mode and watch the delay collapse.
Common mistakes
- Choosing the line after the losses. If you pick h while you're losing, you'll pick whatever justifies how you feel. Set it before the first bet, from the simulated run lengths.
- Treating a losing run as proof. Twelve losers at 3.0 feel like the end of the world and barely move the CUSUM. Know your normal losing runs in advance (Lesson 6.4).
- Resetting the chart when it gets uncomfortable. Restarting at zero because "the new season is different" throws away the evidence. Only reset after a real decision, such as a rebuilt model tested on unseen data.
- Watching P&L instead of CLV. Profit is the noisiest thing you can measure. CLV answers the same question more than ten times sooner.
- Arguing with the alarm. The point of deciding in advance is to remove sentiment. When the line is crossed, stop or cut stakes, then investigate. Don't keep betting while you look for reasons.
Edges fade because markets learn: see pitfall 3 in why good models still lose money.